Session C5: Bose Gases

Contact Measurements on Atomic BEC

For ultracold fermions, a powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with zero-range interactions [1]. An interesting question is whether these ideas and the concept of the contact can be extended to bosons, where issues include the decreasing stability of BECs with increasing repulsive interactions and the possibility of three-body interactions. We present measurements of the contact, using RF spectroscopy, for an $^{85}$Rb atomic Bose-Einstein condensate (BEC) near a Feshbach resonance. To connect our measurements of the contact to three-body interactions, we located an Efimov resonance in $^{85}$Rb atoms with loss measurements and thus determine the three-body interaction parameter. \\[4pt] [1] S. Tan, Ann. Phys. {\bf323}, 2971 (2008)\\[0pt] [2] E. Braaten, D. Kang, and L. Platter, Phys. Rev. Lett. {\bf106}, 153005 (2011).   

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective two-, three-, and four-body interactions for $N$ neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming two-body interactions modelled with the combination of a zero-range and energy-dependent pseudopotential, and working to third-order in the free-space scattering length $a$ at zero collision energy. The results account for quantum fluctuations to excited orbitals and finite-range effects. We show that the effective four-body interaction energy is $U_4(\omega)=+(2.43317...)[a/\sigma ]^3+\mathcal{O}(a^4)$, where $\omega$ and $\sigma$ are the harmonic oscillator frequency and its corresponding length, respectively. After renormalization the effective three-body interaction energy is $U_3(\omega) =-(0.85576...)[a/\sigma]^2 +2.7921(1)[a/\sigma]^3+\mathcal{O}(a^4)$. In addition, we have performed independent numerical simulations for a finite-range boson-boson potential and comparison to the zero-range predictions reveals that finite-range effects must be taken into account. In particular, we show that the energy-dependent pseudopotential captures the finite-range physics and in combination with multi-body effective interactions gives excellent agreement to the numerical simulations.   

Nature of 3D Bose gases near Feshbach Resonance

we explore the nature of 3D Bose gases at large positive scattering lengths via resummation of dominating processes involving a minimum number of virtual atoms. We focus on the energetics of Bose gases beyond the usual dilute limit. We also ?nd that an onset instability sets in at a critical scattering length beyond which the near-resonance Bose gases become strongly coupled to molecules and lose the metastability. Near the point of instability, the chemical potential reaches a maximum and the e?ect of the three-body forces can be estimated to be within a few percent.   

Narrow Feshbach Dance of Two Trapped Atoms

Near a narrow Feshbach resonance (with magnetic field width 10 mG or smaller) the ultra-cold atom interactions acquire an effective range that can be comparable to the average inter-particle distance. Although requiring a more accurate magnetic field control than their broad counterparts, the narrow Feshbach resonances can free cold atom physics from its straightjacket of the contact interaction paradigm. The finite-range effects can give rise to roton features in the phonon dispersion of dilute Bose-Einstein condensates (BEC's) and BEC's can support a ground state with modulated density patterns that breaks translational symmetry. We show that the finite range interaction is the consequence of the time-delay in atom-atom collisions. The narrow regime is also the parameter region in which the interacting atoms can spend a significant fraction of their time in the spin-rearranged (also called ``closed'') channel. To study the interaction physics we describe two atoms in a harmonic trap, interacting near a narrow resonance. We find the fraction of time that the atoms spend in the closed channel at fixed magnetic field and we study the time evolution of this system under conditions of a time-varying magnetic field.   

Expansion Dynamics of a Ring Bose--Einstein Condensate

We studied the dynamics of BECs when released from a ring trap under conditions similar to those that obtained in a recent experiment done at NIST. In that experiment a ring--shaped BEC was formed in an all--optical trap created by intersecting a horizontal light sheet and a vertical Laguerre-Gaussian beam. Condensates were created in these traps and then ``stirred'' by applying Raman pulses having orbital angular momentum (OAM). We modeled the dynamics of condensates formed under these conditions by first solving the 2D time--dependent Gross--Pitaevskii equation (GPE) in imaginary time to obtain the initial condensate shape. We accounted for the OAM by applying a phase imprint to this wave function and then propagated it using the GPE in real time with the trap off. We found that, after release, the condensate expands both inward and outward. When no OAM was applied, this inward expansion causes the hole in the ring to close up entirely in turn causing a buildup of atom density there. Inflow and outflow of atoms from the center caused expanding interference rings to form. With non-zero applied initial OAM similar behavior was observed except that the central hole never closes with hole size increasing with increasing initial OAM. We compare our results with the   

2D Bose--Einstein Condensate Expansion Variational Model

We developed a set of coupled equations to approximate the dynamics of an expanding Bose-Einstein condensate (BEC) properly described by the 3D Gross--Pitaevskii equation (GPE). These equation apply to the case where the condensate is initially confined strongly in one dimension and only weakly in the plane transverse to this direction. The equations were derived using a hybrid Lagrangian Variational Method (LVM) where the trial wave consisted of a completely unspecified function of the coordinates in the plane of weak confinement multiplied by a gaussian function of the transverse coordinate whose width and quadratic phase are variational parameters. The resulting equations consist of a 2D GPE whose nonlinear term is inversely proportional to the time-dependent transverse gaussian width coupled to an equation of motion for the width. The equation of motion for the gaussian width contains a term in which the integral of the fourth power of the 2D GPE solution appears. This factor represents the interaction energy of the confined 2D BEC. This method is applied to model recent experiment with BECs confined in ring--shaped potentials and the solutions are compared to solutions of the full 3D GPE as well as to the results of these experiments.   

Effective interactions of ultracold bosons in anisotropic and anharmonic potentials

We have recently calculated effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in an isotropic (spherical) harmonic trap. But for the important case of optical lattice potentials these results provide only a rough estimate of the effective multibody interactions in the small scattering length regime. In this talk I will extend our model and results to anisotropic and anharmonic potentials. For example, we find anharmonic corrections as large as 30-40{\%} for the effective three-body interaction strength in typical optical lattice potentials. I also discuss non-perturbative behaviors of the multibody interactions.   

Construction of analytical many body wave functions for correlated bosons in a harmonic trap

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions, and respects the analytically known limits of zero and infinite repulsion for arbitrary number of particles. For intermediate interaction strengths we demonstrate, that the energies, as well as the reduced densities of first and second order, are in excellent agreement with large scale numerical calculations.   

Particle losses in Bose-Einstein condensates

The two mode coherent atomic state, so called SU(2) state, evolves in the presence of particle interactions to highly entangled state. The Fisher information increases in the evolution to its maximal possible value. Thus, the system may be useful in the interferometry. Here we study its Fisher information decay due to particle losses. We explain in details new phenomena caused by these processes and finally their effect on the ``usefulness'' of two mode Bose-Einstein condensate for ultra precise measurements.